A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes
A (k ,r)-arc is a set of k points of a projective plane PG(2,q) such that some r, but no r + 1 of them, are collinear. The (k ,r)-arc is complete if it is not contained in a (k + 1,r)-arc. In this paper we give geometrical construction of complete (k <sub>r </sub>,r)-arcs in PG(2...
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| Format: | Article |
| Language: | Arabic |
| Published: |
Mosul University
2018-01-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_163568_dfa566cfb0bd86c7e2bb297ec6cc65cf.pdf |
| _version_ | 1828475980607389696 |
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| author | Nada Kasm Yahya |
| author_facet | Nada Kasm Yahya |
| author_sort | Nada Kasm Yahya |
| collection | DOAJ |
| description | A (k ,r)-arc is a set of k points of a projective plane PG(2,q) such that some r,
but no r + 1 of them, are collinear. The (k ,r)-arc is complete if it is not contained in
a (k + 1,r)-arc.
In this paper we give geometrical construction of complete (k <sub>r </sub>,r)-arcs in PG(2,7),
r = 2,3,…, 7, and the related projective [n,3,d]<sub>7</sub> codes. |
| first_indexed | 2024-12-11T06:21:58Z |
| format | Article |
| id | doaj.art-27566ee40d454fa596994245fb6f48d6 |
| institution | Directory Open Access Journal |
| issn | 1815-4816 2311-7990 |
| language | Arabic |
| last_indexed | 2024-12-11T06:21:58Z |
| publishDate | 2018-01-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj.art-27566ee40d454fa596994245fb6f48d62022-12-22T01:17:48ZaraMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902018-01-01121244010.33899/csmj.2018.163568163568A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 CodesNada Kasm Yahya0Department of Mathematics College of Education for Pure Science University of Mosul, Mosul, IraqA (k ,r)-arc is a set of k points of a projective plane PG(2,q) such that some r, but no r + 1 of them, are collinear. The (k ,r)-arc is complete if it is not contained in a (k + 1,r)-arc. In this paper we give geometrical construction of complete (k <sub>r </sub>,r)-arcs in PG(2,7), r = 2,3,…, 7, and the related projective [n,3,d]<sub>7</sub> codes.https://csmj.mosuljournals.com/article_163568_dfa566cfb0bd86c7e2bb297ec6cc65cf.pdfprojective planecomplete arcscodes |
| spellingShingle | Nada Kasm Yahya A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes Al-Rafidain Journal of Computer Sciences and Mathematics projective plane complete arcs codes |
| title | A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes |
| title_full | A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes |
| title_fullStr | A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes |
| title_full_unstemmed | A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes |
| title_short | A Geometric Construction of Complete (kr ,r)-arcs in PG(2,7) and the Related projective [n,3,d]7 Codes |
| title_sort | geometric construction of complete kr r arcs in pg 2 7 and the related projective n 3 d 7 codes |
| topic | projective plane complete arcs codes |
| url | https://csmj.mosuljournals.com/article_163568_dfa566cfb0bd86c7e2bb297ec6cc65cf.pdf |
| work_keys_str_mv | AT nadakasmyahya ageometricconstructionofcompletekrrarcsinpg27andtherelatedprojectiven3d7codes AT nadakasmyahya geometricconstructionofcompletekrrarcsinpg27andtherelatedprojectiven3d7codes |